The present invention relates to a tool compensation method and, more particularly, to a tool compensation method suitable for applications in which a workpiece is cut by a tapered tool.
Numerical control (NC) systems usually have a tool compensation function. Tool compensation corrects a cutting error due to a tool radius by defining as the passage of movement of a tool center a path that is displaced a distance equal to the tool radius rightward or leftward from a programmed path.
Assuming that there are two programmed paths defined along straight lines L.sub.1, L.sub.2 extending at an angle .alpha. ranging from 90.degree. to 180.degree. as shown in FIG. 1(a), the process of tool compensation is carried out as follows: A movement command for a current block b.sub.1 and a movement command for a next block b.sub.2 are read in advance, and straight lines L.sub.1 ', L.sub.2 ' are determined which are offset a tool radius r.sub.1 from straight lines L.sub.1, L.sub.2, respectively, in the current block b.sub.1 and the next block b.sub.2. The coordinates of a point S.sub.1 where the straight lines L.sub.1 ', L.sub.2 ' intersect are then computed. By moving the tool from a final point S.sub.0 in a previous block to the point S.sub.1 through pulse distribution, the center of the tool follows a passage that is offset a distance equal to the radius r.sub.1 from the properly commanded programmed path for thereby cutting the workpiece. FIG. 1(b) is illustrative of a process of tool compensation performed when the angle .alpha. is smaller than 90.degree..
Where NC systems have such a tool compensation function, programming is quite simple as it is not necessary to take into account the tool radius in preparing an NC data tape. When the tool radius varies due to wear or use of a different tool, the workpiece can be cut correctly by using a tool radius setting dial on an NC system panel to make a tool radius setting, or supplying a tool radius input through an MDI (manual data input) terminal.
However, the above discussed tool compensation method is applicable only to cutting operations using tools having a radius r constant in the axial direction as shown in FIGS. 2(a) through 2(c). As illustrated in FIG. 3, when a tool TL having a radius r is moved in the direction of the arrow A along a straight line LN and a curved line CV to cut surfaces CS.sub.1, CS.sub.2, a workpiece WK can be cut to a desired contour simply by offsetting the tool center a distance equal to the radius r from the straight line LN and the curved line CN even if the workpiece WK has nonparallel surfaces PS.sub.1, PS.sub.2. With the tool TL having the constant radius r, therefore, the distance by which the tool center is offset can be kept constant at all times irrespective of the depth by which the tool cuts into the workpiece, or even when the upper and lower workpiece surfaces PS.sub.1, PS.sub.2 do not lie parallel to each other.
Numerical control has found increasing use recently for cutting three-dimensional shapes, particularly dies. Tapered tools TTL having tapers TP, as shown in FIGS. 4(a) and 4(b), are used more frequently for cutting dies. Such tapered tools caused no problem as long as they cut workpieces with their tips. However, when their tapered surfaces are employed to form workpiece profiles, the tapered tools are unable to effect correct cutting under the conventional tool compensation control method since the tool radius varies in the axial direction.